A376500 Primes that contain at least one even digit and two different odd digits where any permutation of the odd digits leaving the even digits fixed produces a prime.

107, 149, 167, 239, 293, 347, 389, 419, 491, 613, 619, 631, 691, 701, 709, 743, 761, 769, 907, 941, 967, 983, 1009, 1013, 1019, 1031, 1049, 1063, 1091, 1123, 1223, 1229, 1249, 1289, 1321, 1429, 1487, 1499, 1609, 1627, 1669, 1823, 1847, 2113, 2131, 2143, 2237, 2239, 2273, 2293, 2309, 2311, 2341

Offset: 1

Author

Enrique Navarrete, Sep 25 2024

Keywords

• nonn
• base

Comments

The primes in the sequence cannot contain 5.

Examples

			1013 is a term since the permutations of the odd digits that leave the even digits fixed give 1031 and 3011, which are also prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A003459, A376501, A376502.

Programs

Maple

filter:= proc(n) local L,oddi,eveni,xeven,i;
 if not isprime(n) then return false fi;
 L:= convert(n,base,10);
 if member(5,L) then return false fi;
 oddi,eveni:= selectremove(t -> L[t]::odd,[$1..nops(L)]);
 if nops(eveni) = 0 or nops(convert(L[oddi],set))<2 then return false fi;
 xeven:= add(10^(i-1)*L[i],i=eveni);
 andmap(t -> isprime(xeven+add(10^(oddi[i]-1)*L[t[i]],i=1..nops(oddi))), combinat:-permute(oddi))
end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Oct 23 2024